Lamps floating on a lake!

Electricity and Magnetism Level 5

On a summer night PX company decided to open their new branch of decorating lakes they distributed many lamps on alhwiz lake. there are N lamps! these lamps are connected with batteries and each lamp has an electric power of 1 KW. these lamps are distributed uniformly across the lake's surface. Sami has decided to take his girl-friend on a picnic using his Airship! he took her to this lake to show her how much he loves her! and pretended that he has made this for her. Unfortunately she doesn't believe him and she asks him about the number N of these lamps on the lake! he doesnt have much time to count them so he calls you and offer you 10K bucks if you can help him!

there is a sensor of light intensity on the airship measuring the light intensity coming from the lake to be 23.6 W. the lake's raidius is 100m and the airship's height is 100 m . Neglect the Interference and Diffraction effects! what is N? if you yielded non integer value take the floor of it !

Assume that each point of the surface of the lake emits the same amount of energy as any other point!

The answer is 170.

1 solution

Jafar Badour
May 7, 2016

A is the power transferred by the emitted light particles from the lamps per unit area $A = \frac{N *1000}{\pi R^2}$

the power observed from the airship is calculated by

$dp=\frac{ Ar dr d\theta } { r^2 + h^2 }$

thus

$p= 2\pi A ln ( \frac{R^2 + h^2}{h^2})$

$23.6= 2\pi A ln ( \frac{R^2 + h^2}{h^2} )\rightarrow 23.6=\frac{1}{R^2} 2N*1000* ln ( \frac{R^2 + h^2}{h^2} )$

so $N= \frac{23.6*10^4}{2*ln(2)*1000} =170.23$

Lamps floating on a lake!

The answer is 170.

1 solution

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